According to U.S. Energy Information Administration, heating, ventilation, and cooling (HVAC) accounted for 3,856 billion kWh, or 36 percent of the electricity consumed by U.S. households in 2011. Central air-conditioning and refrigeration alone accounted for 30 percent of the total electricity used in homes. Improved refrigeration technology is of major importance and, potentially, a big part of the solution to the energy crisis.
There are several refrigeration technologies, such as vapor-compression refrigeration and magnetic refrigeration. In some implementations, magnetic refrigeration uses the magnetocaloric effect in which an active magnetocaloric material is exposed to an external magnetic field. The isothermal entropy change and the adiabatic temperature change are two important parameters that characterize and quantify the magnetocaloric effect. An integrated Maxwell relation determines the isothermal entropy change, ΔS. The Maxwell relation that originates from the analytic properties of the Gibbs free energy can be expressed as follows:
                                          Δ            ⁢                                                  ⁢            S                    =                                    μ              0                        ⁢            V            ⁢                                          ∫                                  H                  i                                                  H                  f                                            ⁢                                                                    ∂                    M                                                        ∂                    T                                                  ⁢                                  ⅆ                  H                                                                    ,                            (                  Equ          .                                          ⁢          1                )            where Hi,f are the initial (typically zero) and final applied magnetic field, M is the magnetization, V is the volume of the active magnetocaloric material, and μ0 is the vacuum permeability. Equation 1 is valid in situations where the mixed second-order derivatives of the Gibbs free energy exist and the order of differentiation can be exchanged. This is the case in general, with the exception of first-order phase transitions, where the entropy change at the transition can be calculated with the help of the Clausius-Clapeyron equation.